Start by heating your soup pot over medium heat. Add the ground beef or lamb and cook it until nicely browned. I like breaking it up with a wooden spoon to get it evenly cooked. Drain most of the fat, but leave a tablespoon or two for flavor.
Next, toss in the chopped onion, celery, carrots, and garlic. Sauté everything for about 5 minutes. The veggies should soften and your kitchen will already smell like something amazing is cooking.
Now, stir in the tomato paste, Worcestershire sauce, thyme, rosemary, and smoked paprika. These ingredients bring deep, savory notes to the soup. Mix until the veggies are well-coated.
Pour in your broth and bring it to a gentle simmer. I let it cook for 20 minutes, stirring occasionally. Just before it's done, I add the frozen peas—they stay vibrant and slightly crisp this way.
While the soup is simmering, boil your cubed potatoes in another pot until tender (about 12–15 minutes). Drain and mash them with butter, milk, salt, and pepper. I love how creamy they turn out with a splash of heavy cream.
Ladle the soup into bowls and top each with a scoop of mashed potatoes. Sometimes I gently swirl them into the soup so I get creamy bites with every spoonful. Sprinkle with parsley or shredded cheese for a beautiful finish.